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Cayley diagram

D5×Dic7 #63303

order280
isoclinismisoclinic class of D5×D7
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

direct productD5×Dic7

Splittings

derived, HallC5×C7 ⋊ C2×C4
SylowC7 ⋊ C4×D5
SylowC5 ⋊ C2×Dic7

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D5×D7
commutator, hypocenterC5×C7C2×C4
Fitting, socle, cosocleC2×C5×C7C22
prime radicalC2×C7×D5C2
LCSG ▷ C5×C7
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 140

A minimal faithful permutation representation — 2 generators on 16 points:

(2,3)(4,5)(6,7)(8,9,11,12,10)(13,14,15,16);(1,2,4,6,7,5,3)(9,10)(11,12)

Conjugacy classes & character table

40 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×Dic7, Dic7⋊AGL(1,𝔽5), D5×Dic14, …
maximal normal subgroup ofAGL(1,𝔽5)×Dic7, Dic7⋊AGL(1,𝔽5), D5×Dic14, …
maximal quotient ofD5×C7⋊C8, #10587839, Dic5×Dic7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(280, 8);